A174434 Numbers in A093891, but not A005153.

10, 70, 350, 490, 572, 770, 836, 910, 1190, 1330, 1430, 1610, 1750, 1870, 2030, 2090, 2170, 2210, 2470, 2530, 2584, 2590, 2750, 2870, 2990, 3010, 3128, 3190, 3230, 3250, 3290, 3410, 3430, 3710, 3850, 3944, 4130, 4216, 4270, 4550, 4690, 5032, 5390, 5576

Offset: 1

Author

T. D. Noe, Mar 19 2010

Keywords

• nonn

Comments

A number n is in this sequence if the sums of distinct divisors of n form all the primes up to sigma(n), but do not form all the integers up to sigma(n).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A005153, A093891.

Programs

Mathematica

Test[n_] := Module[{d=Divisors[n],t,lim,x}, t=CoefficientList[Product[1+x^i, {i,d}],x]; lim=PrimePi[Length[t]-1]; Count[t[[1+Prime[Range[lim]]]], _?(#>0&)] == lim && Count[t,0] > 0]; Select[Range[1000], Test]